Identity matrix

Identity matrix

In this lesson, we will learn about identity matrices. Identity matrix is an n by n matrix which all entries diagonal from the top left to the bottom right are 1's, and the rest of the entries are 0. There are many types of identity matrices, as listed in the notes section. We will learn how to apply matrix operations with these such as adding, subtracting, and multiplying. Lastly, we will see that identities have a special property. If two matrices are multiplicative inverses, then multiplying them would give an identity matrix.

Lessons

An identity matrix is an nnn by nnn matrix (written as
InI_nI​n​​) where all the entries that is diagonal from the top
left to the bottom right are all 1’s, and the rest of the entries are 0. For example,

are all identity matrices.

1.

a)

The Identity Matrix

b)

Multiplicative Inverses

2.

Matrix Operation with the Identity Matrix
You are given that and . Perform the following matrix operations:

a)

I3⋅A I_3 \cdot A I​3​​⋅A

b)

2A+4I32A+4I_3 2A+4I​3​​

c)

−4B+2I2-4B+2I_2 −4B+2I​2​​

d)

I2⋅B I_2 \cdot B I​2​​⋅B

e)

0⋅I4 0 \cdot I_4 0⋅I​4​​

3.

Multiplicative Inverses
Are the following matrices multiplicative inverses of each other?